Answer: (2) 5 : 3Explanation:-
Let the age of father be X years & the age of his son is Y years.
The sum of the ages of father and his son = 100 years
Then, X + Y = 100 ……………………….. (1)
5 years ago the ratio of their ages = 2 : 1
Then, ( X – 5)/( Y – 5) = 2/1
By cross multiplication,
X – 5 = 2 Y – 10
X – 2 Y = -10 + 5
X – 2 Y = – 5 ………………………. (2)
Solve equation (1) & (2),
Then, X = 65 & Y = 35
Then, the age of father is 65 years & the age of his son is 35 years.
After 10 years,
The age of father is 65 + 10 = 75 & the age of his son is 35+ 10 = 45 years.
The ratio of the age of the father & the age of his son = 75 /45
= 5 : 3
Hence, the answer is (2) 5 : 3.